Estimation of the Error in the Calculation of the Pressure-Strain Term: Application in the Terrestrial Magnetosphere

Calculating the pressure-strain terms has recently been performed to quantify energy conversion between the bulk flow energy and the internal energy of plasmas. It has been applied to numerical simulations and satellite data from the Magnetospheric MultiScale Mission. The method requires spatial gradients of the velocity and the use of the full pressure tensor. Here we present a derivation of the errors associated with calculating the pressure-strain terms from multi-spacecraft measurements and apply it to previously studied examples of magnetic reconnection at the magnetopause and the magnetotail. The errors are small in a dense magnetosheath event but much larger in the more tenuous magnetotail. This is likely due to larger counting statistics in the dense plasma at the magnetopause than in the magnetotail. The propagated errors analyzed in this work are important to understand uncertainties of energy conversion measurements in space plasmas and have applications to current and future multi-spacecraft missions.

Key Points
We estimate the errors on the pressure strain terms calculated from Magnetospheric MultiScale Mission data
The errors are estimated using two methods, standard error propagation from the velocity and temperature errors and a Monte Carlo method
Two applications are given using Magnetospheric MultiScale Mission data at the magnetopause and in the magnetotail of Earth